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Stress derivative issues
Posted Jul 21, 2016, 12:37 p.m. EDT Structural Mechanics Version 5.2 1 Reply
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I am solving a problem that relies on a gradient of hydrostatic stress.
I believe this is expressed as:
d(solid.pm,X)+d(solid.pm,Y)+d(solid.pm,Z).
I have checked the result of this expression against a program I created in MATLAB and the results do not agree (given the same hydrostatic stress profile). I am relatively certain that the profile COMSOL is calculating is incorrect, or at least is very different from what I would expect. I am not exactly sure where I am going wrong as it seems like a rather straightforward implementation. I am rather inexperienced with COMSOL, so any guidance would be appreciated.
I believe this is expressed as:
d(solid.pm,X)+d(solid.pm,Y)+d(solid.pm,Z).
I have checked the result of this expression against a program I created in MATLAB and the results do not agree (given the same hydrostatic stress profile). I am relatively certain that the profile COMSOL is calculating is incorrect, or at least is very different from what I would expect. I am not exactly sure where I am going wrong as it seems like a rather straightforward implementation. I am rather inexperienced with COMSOL, so any guidance would be appreciated.
1 Reply Last Post Jul 22, 2016, 1:29 p.m. EDT
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Posted:
8 years ago
Hi,
As stresses are proportional to strains, they are derivatives of the shape functions. When you try to differentiate them, you get second derivatives, which will have very low accuracy.
Suggestion 1: Use Cubic or Quartic shape functions instead of the default Quadratic.
Suggestion 2: Add an extra degree of freedom for the hydrostatic stress, which you in the weak sense map to solid.pm. In this way you can obtain something more smooth and differentiable.
By the way: A gradient is a vector, your expression is a scalar (the sum of the components of the gradient). It is more probable that you are interested in sqrt(d(solid.pm,X)^2+d(solid.pm,Y)^2+d(solid.pm,Z)^2)
Regards,
Henrik
As stresses are proportional to strains, they are derivatives of the shape functions. When you try to differentiate them, you get second derivatives, which will have very low accuracy.
Suggestion 1: Use Cubic or Quartic shape functions instead of the default Quadratic.
Suggestion 2: Add an extra degree of freedom for the hydrostatic stress, which you in the weak sense map to solid.pm. In this way you can obtain something more smooth and differentiable.
By the way: A gradient is a vector, your expression is a scalar (the sum of the components of the gradient). It is more probable that you are interested in sqrt(d(solid.pm,X)^2+d(solid.pm,Y)^2+d(solid.pm,Z)^2)
Regards,
Henrik